Download Diffusion Tensor Imaging: Concepts and Applications

JOURNAL OF MAGNETIC RESONANCE IMAGING 13:534 –546 (2001)
Original Research
Diffusion Tensor Imaging: Concepts and
Applications
Denis Le Bihan, MD, PhD,1* Jean-François Mangin, PhD,1 Cyril Poupon, PhD,1
Chris A. Clark, PhD,1 Sabina Pappata, MD, PhD,1 Nicolas Molko, MD,1,2 and
Hughes Chabriat, MD1,2
The success of diffusion magnetic resonance imaging
(MRI) is deeply rooted in the powerful concept that during
their random, diffusion-driven displacements molecules
probe tissue structure at a microscopic scale well beyond
the usual image resolution. As diffusion is truly a threedimensional process, molecular mobility in tissues may be
anisotropic, as in brain white matter. With diffusion tensor
imaging (DTI), diffusion anisotropy effects can be fully extracted, characterized, and exploited, providing even more
exquisite details on tissue microstructure. The most advanced application is certainly that of fiber tracking in the
brain, which, in combination with functional MRI, might
open a window on the important issue of connectivity. DTI
has also been used to demonstrate subtle abnormalities in
a variety of diseases (including stroke, multiple sclerosis,
dyslexia, and schizophrenia) and is currently becoming
part of many routine clinical protocols. The aim of this
article is to review the concepts behind DTI and to present
potential applications. J. Magn. Reson. Imaging 2001;13:
534 –546. © 2001 Wiley-Liss, Inc.
THE BASIC PRINCIPLES of diffusion MRI were introduced in the mid-1980s (1–3); they combined NMR imaging principles with those introduced earlier to encode
molecular diffusion effects in the NMR signal by using
bipolar magnetic field gradient pulses (4). Molecular
diffusion refers to the random translational motion of
molecules, also called Brownian motion, that results
from the thermal energy carried by these molecules.
The success of diffusion MRI is deeply rooted in the
powerful concept that during their random, diffusiondriven displacements molecules probe tissue structure
at a microscopic scale well beyond the usual image
resolution: during typical diffusion times of about 50
msec, water molecules (water is the most convenient
molecular species to study with diffusion MRI, but
some metabolites may also be studied) move in the
brain on average over distances around 10 ␮m, bouncing, crossing, or interacting with many tissue compo-
1
Service Hospitalier Frédéric Joliot, CEA, 91406 Orsay, France.
Department of Neurology, Lariboisière Hospital, 75010 Paris, France.
*Address reprint requests to: D.L.B., Service Hospitalier Frédéric Joliot,
CEA, 4, place du Général Leclerc, 91406 Orsay Cedex France.
E-mail: [email protected]
Received July 24, 2000; Accepted August 14, 2000.
2
© 2001 Wiley-Liss, Inc.
nents such as cell membranes, fibers, or macromolecules.
The overall effect observed in a diffusion MRI image
voxel of several mm3 reflects, on a statistical basis, the
displacement distribution of the water molecules
present within this voxel. The observation of this displacement distribution may thus provide unique clues
to the structure and geometric organization of tissues.
MRI is the only means we have to observe diffusion in
vivo noninvasively. Furthermore, MRI provides access
to both superficial and deep organs with high resolution
and does not interfere with the diffusion process itself:
diffusion is an intrinsic physical process that is totally
independent of the MR effect or the magnetic field. This
is not the case for most MRI-accessible parameters,
such as T1 or T2.
Potential clinical applications of water diffusion MRI
were suggested very early (5). The most successful application of diffusion MRI since the early 1990s has
been brain ischemia (6), following the discovery in cat
brain by Moseley et al. that water diffusion drops at a
very early stage of the ischemic event (7). Diffusion MRI
provides some patients with the opportunity to receive
suitable treatment at a stage when brain tissue might
still be salvageable.
Furthermore, diffusion is truly a three-dimensional
process. Hence, molecular mobility in tissues may not
be the same in all directions. This anisotropy may result
from a peculiar physical arrangement of the medium
(such as in liquid crystals) or the presence of obstacles
that limit molecular movement in some directions. As
diffusion is encoded in the MRI signal by using magnetic field gradient pulses (8), only molecular displacements that occur along the direction of the gradient are
visible. The effect of diffusion anisotropy can then easily
be detected by observing variations in the diffusion
measurements when the direction of the gradient
pulses is changed. This is a unique, powerful feature
not found with usual MRI parameters, such as T1 or T2.
Diffusion anisotropy had been observed long ago in
muscle (9). With the advent of diffusion MRI, anisotropy
was also detected in vivo at the end of the 1980s in
spinal cord (10) and brain white matter (11,12). More
recently, diffusion anisotropy has also been seen in rat
brain gray matter (13,14) and in human brain of neo-
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Diffusion Tensor Imaging
535
nates. Diffusion anisotropy in white matter originates
from its specific organization in bundles of more or less
myelinated axonal fibers running in parallel, although
the exact mechanism is still not completely understood
(see below): diffusion in the direction of the fibers is
faster than in the perpendicular direction. It quickly
appeared that this feature could be exploited to map
out the orientation in space of the white matter tracks
in the brain using a color scale, assuming that the
direction of the fastest diffusion would indicate the
overall orientation of the fibers (15).
This pioneering work on diffusion anisotropy really
took off with the introduction of the more rigorous formalism of the diffusion tensor by Basser et al. (16 –18).
With diffusion tensor imaging (DTI), diffusion anisotropy effects in diffusion MRI data could be fully extracted, characterized, and exploited, providing even
more exquisite details of tissue microstructure. Many
studies have been published dealing with the optimization of the MRI sequences necessary to gain access to
the diffusion tensor, the processing and display of DTI
data, and, of course, potential applications. The most
advanced application is certainly that of fiber tracking
in the brain, which, in combination with functional
MRI, might open a window onto the important issue of
connectivity.
The aim of this article is to review the concepts behind
DTI and to present potential applications.
DIFFUSION TENSOR MRI: DATA ACQUISITION
AND PROCESSING
The Diffusion Tensor
With plain diffusion MRI, diffusion is fully described
using a single (scalar) parameter, the diffusion coefficient, D. The effect of diffusion on the MRI signal (most
often a spin-echo signal) is an attenuation, A, which
depends on D and on the “b factor,” which characterizes
the the gradient pulses (timing, amplitude, shape) used
in the MRI sequence (8):
A ⫽ exp共⫺bD兲.
(1)
However, in the presence of anisotropy, diffusion can
no longer be characterized by a single scalar coefficient,
but requires a tensor, D, which fully describes molecular mobility along each direction and correlation between these directions (4) (Fig. 1):
Dxx
D ⫽ Dyx
Dzx
Dxy
Dyy
Dzy
Dxz
Dyz .
Dzz
where bii are the elements of the b matrix (which now
replaces the b factor) expressed in the coordinates of
this reference frame.
In practice, unfortunately, measurements are made
in the reference frame [ x, y, z] of the MRI scanner
gradients, which usually does not coincide with the
diffusion frame of the tissue. Therefore, one must also
consider the coupling of the nondiagonal elements, bij,
of the b matrix with the nondiagonal terms, Dij, (i ⫽ j),
of the diffusion tensor (now expressed in the scanner
frame), which reflect correlation between molecular displacements in perpendicular directions (17):
A ⫽ exp共⫺
冘 冘
bijDij兲
(4)
i ⫽ x,y,z j ⫽ x,y,z
or
A ⫽ exp共⫺bxxDxx ⫺ byyDyy ⫺ bzzDzz
(2)
This tensor is symmetric (Dij ⫽ Dji, with i, j ⫽ x, y, z).
In a reference frame [ x⬘, y⬘, z⬘] that coincides with the
principal or self directions of diffusivity, the off-diagonal
terms do not exist, and the tensor is reduced only to its
diagonal terms, Dx⬘x⬘, Dy⬘y⬘, Dz⬘z⬘, which represent molecular mobility along axes x⬘, y⬘, and z⬘, respectively. The
echo attenuation then becomes:
A ⫽ exp共⫺bx⬘x⬘Dx⬘x⬘ ⫺ by⬘y⬘Dy⬘y⬘ ⫺ bz⬘z⬘Dz⬘z⬘兲
Figure 1. The diffusion tensor, axial slices. Diffusivity along x,
y, and z axes, shown in Dxx (a), Dyy (d), and Dzz (f) images,
respectively, is clearly different in white matter, especially in
the corpus callosum. Nondiagonal images [Dxy (b), Dxz (c), and
Dyz (e)] are not noise images because the x, y, z reference frame
of the MRI scanner does not coincide with the diffusion reference frame of tissues in most voxels.
(3)
⫺ 2bxyDxy ⫺ 2bxzDxz ⫺ 2byzDyz兲.
(5)
Hence, it is important to note that by using diffusionencoding gradient pulses along one direction only, say
x, signal attenuation not only depends on the diffusion
effects along this direction but may also include contribution from other directions, say y and z.
Calculation of b may quickly become complicated
when many gradient pulses are used (20,21), but the
full determination of the diffusion tensor is necessary if
one wants to assess properly and fully all anisotropic
diffusion effects.
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Le Bihan et al.
DTI Data Acquisition
To determine the diffusion tensor fully, one must first
collect diffusion-weighted images along several gradient directions, using diffusion-sensitized MRI pulse sequences (22) such as echoplanar imaging (EPI). As the
diffusion tensor is symmetric, measurements along
only six directions are mandatory (instead of nine),
along with an image acquired without diffusion weighting (b ⫽ 0). A typical set of gradient combinations that
preserves uniform space sampling and similar b values
along each direction is as follows (coefficients for gradient pulses along the (x, y, z) axes, normalized to a given
amplitude, G):
关共1/兹2, 0, 1/兹2兲; 共⫺1/兹2, 0, 1/兹2兲;
共0, 1/兹2, 1/兹2兲; 共0, 1/兹2, ⫺1/兹2兲;
共1/兹2, 1/兹2, 0兲; 共 ⫺ 1/兹2, 1/兹2, 0兲兴.
This minimal set of images may be repeated for averaging, as the signal-to-noise ratio (SNR) may be low
(17,18). Note that it is not necessary (and not efficient in
terms of SNR) to obtain data with different b values for
each direction. A simple calculation (22) shows that, in
the case of scalar diffusion, one gets the best accuracy
on the diffusion coefficient, D, from two acquisitions
when using 2 b factors, b1 and b2, differing by about
1/D (23). In the brain, this translates to (b2 ⫺ b1) ⬇
1000–1500 s/mm2. If more than two acquisitions are to
be used (for averaging purposes), error propagation theory (24) shows that it is better to accumulate n1 and n2
measurements at each of the low and high b factors, b1
and b2, than to use a range of b factors. The accuracy
dD/D is then obtained from the raw image SNR:
dD/D ⫽ 关1/n 1 ⫹ exp关2D共b1 ⫺ b2兲兴/n2兴1/2
⫻ 关SNR 䡠 D共b1 ⫺ b2兲兴.
(6)
In the anisotropic case, this paradigm would be still
useful, but one should bear in mind that D will change
for each voxel according to the measurement direction
(25).
Acquisition performed with linear sets of b value
ranges remains, however, extremely useful to assess
the sequence/hardware performance (stability, eddy
currents, . . . ) (22) or to characterize the diffusion process better, in particular in the presence of multiple
diffusion compartments (see below).
In the case of axial symmetry, only four directions are
necessary (tetrahedral encoding) (26), as suggested in
the spinal cord (27,28). The acquisition time and the
number of images to process are then reduced. In contrast, efforts are now being made to collect data along as
many directions in space as possible to avoid sampling
direction biases. This uniform space sampling paradigm is particularly interesting for fiber tracking applications and provides a gain in SNR (25,29) (Fig. 2 and
see below).
DTI Data Processing
A second step is to estimate the Dij values from the set
of diffusion/orientation-weighted images, generally by
Figure 2. Schemes for directional sampling. Although initial
sampling schemes consisted of six (or even four) directions of
measurements, progress is made in scanning space more uniformly along many directions, especially for fiber orientation
mapping.
multiple linear regression, using Eq. [5]. From the diffusion tensor components, one may calculate indices
that reflect either the average diffusion or the degree of
anisotropy in each voxel (see below). Another step is to
determine the main direction of diffusivities in each
voxel and the diffusion values associated with these
directions. This is equivalent to determining the reference frame [ x⬘, y⬘, z⬘] where the off-diagonal terms of D
are null. This “diagonalization” of the diffusion tensor
provides eigen-vectors and eigen-values, ␭, which correspond respectively to the main diffusion directions
and associated diffusivities (17,18). (The eigen-diffusivities, ␭, are not to be confused with the tortuosity
factors.)
As it is difficult to display tensor data with images
(multiple images would be necessary), the concept of
diffusion ellipsoids has been proposed (17,18). An ellipsoid is a three-dimensional representation of the diffusion distance covered in space by molecules in a given
diffusion time, Td. These ellipsoids, which can be displayed for each voxel of the image, are easily calculated
from the eigen diffusivities, ␭1, ␭2, and ␭3 (corresponding to Dx⬘x⬘, Dy⬘y⬘, and Dz⬘z⬘):
x⬘ 2 /共2␭ 1 T d 兲 ⫹ y⬘ 2 /共2␭ 2 T d 兲 ⫹ z⬘ 2 /共2␭ 3 T d 兲 ⫽ 1
(7)
where x⬘, y⬘, and z⬘ refer to the frame of the main
diffusion direction of the tensor. These eigen diffusivities represent the unidimensional diffusion coefficients
in the main directions of diffusivities of the medium.
Therefore, the main axis of the ellipsoid gives the main
diffusion direction in the voxel (coinciding with the direction of the fibers), while the eccentricity of the ellipsoid provides information about the degree of anisot-
Diffusion Tensor Imaging
537
Figure 3. DTI in normal
brain. The mean diffusivity
(obtained from the trace of
the diffusion tensor) corresponds to the overall water
molecular
displacements,
which are very similar in gray
and white matter. On the
other hand, the volume ratio
index, which reflects anisotropy, varies greatly in gray
and white matter. Anisotropy
is mainly seen in highly oriented white matter tracks.
ropy and its symmetry. (Isotropic diffusion would be
seen as a sphere.) The length of the ellipsoids in any
direction in space is given by the diffusion distance
covered in this direction. In other words, the ellipsoid
can also be seen as the three-dimensional surface of
constant mean squared displacement of the diffusing
molecules.
Recent work has demonstrated the feasibility of DTI
in animal models, as well as in the human brain
(16,26,30,31).
ties (main ellipsoid axes), which is linked to the orientation in space of the structures. These three DTI metaparameters can all be derived from the whole
knowledge of the diffusion tensor. However, due to the
complexity of data acquisition and processing for full
DTI, and the sensitivity to noise of the determination of
the diffusion tensor eigen-values, simplified approaches have been proposed.
EXTRACTING INFORMATION FROM DTI DATA
To obtain an overall evaluation of the diffusion in a
voxel or region, one must avoid anisotropic diffusion
effects and limit the result to an invariant, ie, a quantity
that is independent of the orientation of the reference
frame (18). Among several combinations of the tensor
elements, the trace of the diffusion tensor,
Using DTI, it appears that diffusion data can be analyzed in three ways to provide information on tissue
microstructure and architecture for each voxel (32,33):
The mean diffusivity, which characterizes the overall
mean-squared displacement of molecules (average ellipsoid size) and the overall presence of obstacles to
diffusion; the degree of anisotropy, which describes
how much molecular displacements vary in space (ellipsoid eccentricity) and is related to the presence of
oriented structures; and the main direction of diffusivi-
Mean Diffusivity
Tr共D兲 ⫽ Dxx ⫹ Dyy ⫹ Dzz
(8)
is such an invariant. The mean diffusivity is then given
by Tr(D)/3. A slightly different definition of the trace has
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Le Bihan et al.
proved useful in assessing the diffusion drop in brain
ischemia (34) (Fig. 3 and see below).
Unfortunately, the correct estimation of Tr(D) still
requires the complete determination of the diffusion
tensor. Generally, one cannot simply add diffusion coefficients obtained by separately acquiring data with
gradient pulses added along x, y, and z axes, as these
measured coefficients usually do not coincide with Dxx,
Dyy, and Dzz, respectively (see above). The reason is that
the diffusion attenuation that results, for instance,
from inserting gradients on the x axis (see above) is not
simply A ⫽ exp[ ⫺ bxxDxx], unless diffusion is isotropic
(no nondiagonal terms) or the contribution of the gradient pulses on y and z axes is negligible. (Sequences
can be written that way.)
To avoid this problem and to simplify the approach,
several groups have designed sequences based on multiple echoes or acquisitions with tetrahedral gradient
configurations, so as to cancel nondiagonal term contributions to the MRI signal directly (26,35–37).
RA, a normalized standard deviation, also represents
the ratio of the anisotropic part of D to its isotropic part.
FA measures the fraction of the “magnitude” of D that
can be ascribed to anisotropic diffusion. FA and RA vary
between 0 (isotropic diffusion) and 1(公2 for RA) (infinite
anisotropy). As for VR, which represents the ratio of the
ellipsoid volume to the volume of a sphere of radius 具␭典,
its range is from 1 (isotropic diffusion) to 0, so that some
authors prefer to use (1 ⫺ VR) (39).
Once these indices have been defined, it is possible to
evaluate them directly from diffusion-weighted images,
ie, without the need to calculate the diffusion tensor
(40). For instance, A␴, which is very similar to RA, has
been proposed as (41):
A␴ ⫽
兹冘
2
2
共D i ⫺ 具D典兲 2 ⫹ 共D xy
⫹ D xz
⫹ D 2yz 兲/兹6具D典
i ⫽ x,y,z
(13)
with
具D典 ⫽
Diffusion Anisotropy Indices
Several scalar indices have been proposed to characterize diffusion anisotropy. Initially, simple indices calculated from diffusion-weighted images (10) or ADCs obtained in perpendicular directions were used, such as
ADCx/ADCy (15) and displayed using a color scale.
Other groups have devised indices mixing measurements along x, y, and z directions, such as max[ADCx,
ADCy, ADCz]/min[ADCx, ADCy, ADCz] or the standard
deviation of ADCx, ADCy, and ADCz divided by their
mean value (34). Unfortunately, none of these indices
are really quantitative, as they do not correspond to a
single meaningful physical parameter and, more importantly, are clearly dependent on the choice of directions
made for the measurements. The degree of anisotropy
would then vary according to the respective orientation
of the gradient hardware and the tissue frames of reference and would generally be underestimated. Here
again, invariant indices must be found to avoid such
biases and provide an objective, intrinsic structural
information (38).
Invariant indices are thus made of combinations of
the terms of the diagonalized diffusion tensor, ie, the
eigen-values ␭1, ␭2, and ␭3. The most commonly used
invariant indices are the relative anisotropy (RA), the
fractional anisotropy (FA), and the volume ratio (VR)
indices, defined respectively as:
RA ⫽ 兹共␭1 ⫺ 具␭典兲2 ⫹ 共␭2 ⫺ 具␭典兲2 ⫹ 共␭3 ⫺ 具␭典兲2/兹3具␭典
(9)
where
具␭典 ⫽ 共␭ 1 ⫹ ␭ 2 ⫹ ␭ 3 兲/3.
(10)
VR ⫽ ␭1␭2␭3/具␭典3.
D i /3
(14)
Also, images directly sensitive to anisotropy indices, or
anisotropically weighted images, can be obtained (42).
Finally, the concept of these intravoxel anisotropy indices can be extended to a family of intervoxel or “lattice”
measures of diffusion anisotropy, which allows neighboring voxels to be considered together, in a region of
interest, without losing anisotropy effects resulting
from different fiber orientations across voxels (39). Clinically relevant images of anisotropy indices have been
obtained in the human brain (31,43) (Figs. 3, 4; Table 1).
Fiber Orientation Mapping
The last family of parameters that can be extracted from
the DTI concept relates to the mapping of the orientation in space of tissue structure. The assumption is that
the direction of the fibers is colinear with the direction
of the eigen-vector associated with the largest eigen
diffusivity. This approach opens a completely new way
to gain direct and in vivo information on the organization in space of oriented tissues, such as muscle, myocardium, and brain or spine white matter, which is of
considerable interest, clinically and functionally. Direction orientation can be derived from DTI directly from
diffusion/orientation-weighted images or through the
calculation of the diffusion tensor. A first issue is to
display fiber orientation on a voxel-by-voxel basis. The
use of color maps has first been suggested (15), followed
by representation of ellipsoids (18,39), octahedra (44),
or vectors pointing in the fiber direction (45,46) (Figs.
5, 6).
APPLICATIONS
FA ⫽ 兹3关共␭1 ⫺ 具␭典兲2 ⫹ 共␭2 ⫺ 具␭典兲2 ⫹ 共␭3 ⫺ 具␭典兲2兴/
兹2共␭12 ⫹ ␭22 ⫹ ␭32兲.
冘
i ⫽ x,y,z
(11)
(12)
It is important to notice that diffusion imaging is a truly
quantitative method. The diffusion coefficient is a physical parameter that directly reflects the physical properties of the tissues, in terms of the random transla-
Diffusion Tensor Imaging
539
Figure 4. Comparison of various anisotropy indices. a: Simple anisotropy
index given by: (␭/具␭典 ⫺ 1)/2. b: Relative anisotropy index (RA). c: Volume
ratio index (VR). d: Fractional anisotropy index (FA).
tional movement of the molecules under study (most
often water molecules, but some metabolites have been
studied as well; see below). Diffusion coefficients obtained at different times in a given patient or in different
patients or in different hospitals can be compared, in
principle, without any need for normalization.
However, most diffusion measurements in biologic
tissues refer to an apparent diffusion coefficient, and it
is generally considered that diffusion in the measurement volume (voxel) has a unique diffusion coefficient.
In reality, most tissues are made of multiple subcompartments, at least the intra- and the extracellular compartments, and the ADC that is measured could depend
on the range used for the b values, as measurements
with low b values would be more sensitive to fast diffusion components. The ideal approach would be to separate all subcompartments by fitting the data with a
multiexponential decay. Unfortunately, the values for
Di are often low and not very different from each other,
so that very large b values and very high SNRs would be
required.
Table 1
Diffusion Coefficients of Water in Human Brain (⫻10⫺3 mm2/s)*
Cerebrospinal fluid (CSF)
Gray matter (frontal cortex)
Caudate nucleus
White matter
Pyramidal tract
Corpus callosum (splenium)
Internal capsule
Centrum semiovale
Mean
diffusivity
Anisotropy
(1-volume
ratio)
3.19 ⫾ 0.10
0.83 ⫾ 0.05
0.67 ⫾ 0.02
0.02 ⫾ 0.01
0.08 ⫾ 0.05
0.08 ⫾ 0.03
0.71 ⫾ 0.04
0.69 ⫾ 0.05
0.64 ⫾ 0.03
0.65 ⫾ 0.02
0.93 ⫾ 0.04
0.86 ⫾ 0.05
0.70 ⫾ 0.08
0.27 ⫾ 0.03
*Measurements were obtained in normal volunteers using diffusion
tensor MRI (from ref. 31).
Two diffusion compartments have been found in the
rat brain (47). Assignment of these compartments to
extra- and intracellular water is not, however, straightforward, as the values found for the two compartments
are apparently opposite to the known volume fractions
for the intra- and extracellular spaces (82.5% and
17.5%, respectively). This discrepancy may partially result from the exchange that occurs between compartments. It has been shown that in this case, if the residence rate in each compartment is considered, the
contribution of the fast diffusing component is overestimated (48). It is thus not certain whether the two
compartments that have been observed correspond to
the intra- and extracellular compartments.
In any case, it is clear that the “apparent” diffusion
coefficient depends on the range used for the b values
and would not reflect univocally diffusion in the tissue.
Measurements with low b values (less than 1000
s/mm2) would then be more sensitive to fast diffusion
components (possibly as the extracellular compartment). In clinical studies and most animal experiments,
especially when data are fitted to a single exponential,
diffusion patterns observed in tissues have thus to be
explained by features of the extracellular space, although this compartment is physically small. Changes
in the ADC calculated in these conditions should thus
be interpreted in terms of changes in the diffusion coefficient of the extracellular space (tortuosity) and in its
fractional volume relative to the intracellular volume.
This explains why diffusion has appeared as a sensitive
marker of the changes in the extracellular/intracellular
volume ratio, as observed in brain ischemia, spreading
depression (49 –51), status epilepticus (52), and extraphysiologic manipulations of the cell size through osmotic agents (53). Using large b values, it could become
possible to assess separately the intra- and extracellular compartments and their relative volumes, as has
540
Le Bihan et al.
Figure 5. Two-dimensional display of the diffusion tensor. A: Projection of the main eigen-vector on a high-resolution T2weighted image. B: Representation of the main eigen-vector direction using a color scale (red ⫽ x axis, green ⫽ y axis, blue ⫽ z
axis).
been suggested in vitro (54), but also in vivo in the rat
(47) and human brain (55,56).
Brain Ischemia
During the acute stage of brain ischemia, water diffusion is decreased in the ischemic territory by as much
as 50%, as shown in cat brain models (57). This diffusion slowdown is linked to cytotoxic edema, which re-
sults from the energetic failure of the cellular membrane Na/K pumping system. The exact mechanism of
the diffusion decrease is still unclear. Increase of the
slow diffusion intracellular volume fraction, changes in
membrane permeability (58), and shrinkage of the extracellular space resulting in increased tortuosity for
water molecules (59,60) have been suggested. Diffusion
MRI has been extensively used in animal models to
establish and test new therapeutic approaches. These
results have been confirmed in human stroke cases,
offering the potential to highlight ischemic regions
within the first hours of the ischemic event, when brain
tissue might still be salvageable (6,61), and well before
conventional MRI becomes abnormal (vasogenic edema). Combined with perfusion MRI, diffusion MRI is
under clinical evaluation as a tool to help clinicians
optimize their therapeutic approach to individual patients (62), to monitor patient progress on an objective
basis, and to predict clinical outcome (63– 66). Anisotropic diffusion effects in diffusion-weighted images
may sometimes mimic ischemic regions, especially near
ventricular cavities: if diffusion sensitization is made in
only one direction, which is perpendicular to the white
matter fibers, bright (low diffusion) spots will be visible
on the images. It is, therefore, a good practice to use
images of the mean diffusivity (or the trace of the diffusion tensor) to remove these artifacts (34) (Fig. 7).
Brain White Matter
Figure 6. Three-dimensional display of the diffusion tensor.
Main eigen-vectors are shown as cylinders, the length of which
is scaled with the degree of anisotropy. Corpus callosum fibers
are displayed around ventricles, thalami, putamen, and caudate nuclei.
In the white matter, diffusion MRI has already shown
its potential in diseases such as multiple sclerosis (67).
However, DTI offers more through the separation of
mean diffusivity indices, such as the trace of the diffusion tensor, which reflects overall water content, and
anisotropy indices, which point toward myelin fiber integrity. Examples include multiple sclerosis (68 –71),
leukoencephalopathy (72), Wallerian degeneration, Alz-
Diffusion Tensor Imaging
541
Figure 7. DTI in acute stroke (7 hours). Acute ischemic regions appear bright in diffusion-weighted images. As normal white
matter regions may also appear bright in some orientations (indicated by the bold arrows) due to anisotropic diffusion effects,
the use of images weighted by the trace of the diffusion tensor is more adequate (the ischemic lesion is indicated by the thin
arrow). (Courtesy of C. Oppenheim, MD. Salpêtrière Hospital, Paris)
heimer’s disease (73,74), and CADASIL (Cerebral Autosomal Dominant Arteriopathy with Subcortical Infarcts
and Leucoenuphalopathy) (75). (Fig. 8).
It has been shown that the degree of diffusion anisotropy in white matter increases during the myelination
process (43,76,77), and diffusion MRI could be used to
assess brain maturation in children (78), newborns, or
premature babies (43,79). Abnormal connectivity in
white matter based on DTI MRI data has also been
reported in frontal regions in schizophrenic patients
(80,81) and in left temporo-parietal regions in dyslexic
adults (82). The potential of diffusion MRI has also been
studied in brain tumor grading (83– 85), trauma (86),
hypertensive hydrocephalus (87), AIDS (88), eclampsia
(89), leukoaraiosis (90,91), migraine (92), and the spinal cord in animals (27,66,93,94) and humans (95,96).
The concepts of restriction, hindrance, tortuosity,
and multiple compartments are particularly useful for
understanding diffusion findings in brain white matter
(33). The facts are that: a) water diffusion is highly
anisotropic in white matter (10 –12); b) such anisotropy
has been observed even before fibers are myelinated,
although to a lesser degree (43,43,77,97–102); and c)
the ADCs measured in parallel and perpendicularly to
the fibers do not seem to depend on the diffusion time
(103,104) at least for diffusion times longer than 20
msec (Fig. 8).
Initial reports suggested that the anisotropic water
diffusion could be explained on the basis that water
molecules were restricted in the axons (anisotropically
restricted diffusion) due to the presence of the myelin
sheath (105,106). However, although restricted diffusion has been seen for intraaxonal metabolites, such as
NAA (N-Acetyl-Aspartate), or for truly intraaxonal water
(107), it now appears that most studies performed with
relatively low b values are mostly sensitive to the extracellular, interaxonal space. In this condition, diffusion
anisotropy in white matter should be linked to the
anisotropic tortuosity of the interstitial space between
fibers: diffusion is more impeded perpendicularly to the
542
Le Bihan et al.
Figure 8. DTI in CADASIL, a genetic disease that results in
ischemia of white matter due to abnormalities in microvasculature. White matter lesions, which appear well before clinical
findings, are seen as areas with increased mean diffusivity
(bottom row) in white matter regions that extend well beyond
T2 abnormalities. Decreased anisotropy can also be seen on
VR diffusion images (not shown). Top row, T2-weighted MRI.
Figure 9. Brain fiber tracking.
The most challenging application
of DTI is brain connectivity
through the visualization of white
matter tracks. Using an ad hoc algorithm, it is possible to infer connectivity between neighboring
principal eigen-vector voxels (as
seen in Fig. 6). A: Callosum fibers
around ventricles. B: Occipitofrontal tracks crossing a “seeding”
region of interest (ROI input).
Diffusion Tensor Imaging
543
fibers mainly because of their geometric arrangement
(103) (Fig. 7).
Considering a bundle where fibers are organized in
the most compact way, molecules would have to actually travel over a distance of ␲d/2, where d is the fiber
diameter, to apparently diffuse over a distance equal to
the fiber diameter. Therefore, on average, the ADC measured perpendicularly to the fibers would then be reduced, whatever the diffusion time, to:
ADC ⫽ 共2/␲兲2D0 ⬇ 0.4 D0
(15)
where the reference value, D0, is the diffusion value
measured in parallel to the fibers. This ratio of about
0.4 fits reasonably well with literature data (103), although much larger ratios have been reported (39). This
rough model also implies that the tortuosity factor
would be anisotropic in white matter with a ␭perpendicular/
␭parallel ratio of ␲/2(⬇1.15). Unfortunately, no systematic measurements of ␭ have been made yet in white
matter using ionic extracellular tracers (108,109), although anisotropy has been seen (110). Another interesting point about this model is that it is compatible
with the fact that no true restricted effects are observed
when the diffusion time is increased, as there are no
actual boundaries to diffusing molecules. Also, the parallel organization of the fibers may be sufficient to explain the presence of anisotropy before myelination.
However, as the axonal membranes should be more
permeable to water than the myelin sheaths, the degree
of anisotropy should be less pronounced in the absence
of myelin, as significant exchanges with the axonal
spaces should occur. Oriented filaments within the axoplasm do not seem do play an important role (111).
Brain Connectivity
An important potential application of DTI is the visualization of anatomic connections between different parts
of the brain on an individual basis. Studies of neuronal
connectivity are tremendously important for interpreting functional MRI data and establishing how activated
foci are linked together through networks (112,113).
This issue is difficult, as one has to infer continuity of
fiber orientation from voxel to voxel. This orientation
may vary due to noisy data, and one has to deal with
fiber merging, branching, dividing etc. Also, several fascicles may cross in a given voxel, which cannot be detected with the diffusion tensor approach in its present
form (114). On the other hand, structures that exhibit
anisotropic diffusion at the molecular level can be isotropically oriented at the microscopic level, resulting in
a “powder average” effect that is difficult to resolve
(115). The plot of the signal attenuation versus b may
not be linear in this case (116). This deviation from
linearity can be ascribed, however, to anisotropy and
not to restricted diffusion, because the diffusion measurements are independent of the diffusion time. Several groups have recently approached the difficult problem of inferring connectivity from DTI data, from the
dead rat brain (117) to the living human brain (118 –
122) (Fig. 9).
Fiber orientation mapping and connectivity studies
derived from anisotropic diffusion in white matter will
clearly benefit from a better understanding of the respective contributions of intraaxonal and extraaxonal
compartments to anisotropy mechanisms (123).
Body
Outside the brain, diffusion has been more difficult to
use successfully, because of the occurrence of strong
respiratory motion artifacts in the body and the short
T2 values of body tissues, which require shorter TE
than in the brain and thus leave less room for the
diffusion gradient pulses. These obstacles, however,
can sometimes be overcome with ad hoc MR sequences
and hardware. A potential for tissue characterization
has been shown in the extremity muscles (124), the
spine (125,126), the breast (127–129), the kidney, and
the liver (130 –133). As for DTI, muscle fiber orientation
can be approached in organs such as the tongue (134)
or the heart. Myocardium DTI (135) has the tremendous potential of providing data on heart contractility, a
very important parameter, but it remains technically
very challenging to perform in vivo due to heart motion.
CONCLUSIONS
Many tissue features at the microscopic level may
influence NMR diffusion measurements. Many theoretical analyses on the effect of restriction, membrane
permeability, hindrance, anisotropy, or tissue
inhomogeneity have underlined how much care is necessary
to interpret diffusion NMR data properly and infer
accurate information on microstructure and microdynamics in vivo in biologic systems. Even at its current stage, DTI is the only approach available to track
brain white matter fibers noninvasively. DTI should
thus have a tremendous impact on brain function
studies. DTI has also been used to demonstrate subtle abnormalities in a variety of diseases including
multiple sclerosis and schizophrenia and is currently
becoming part of many routine clinical protocols.
With the development of powerful improvements to
DTI, such as diffusion spectroscopy of metabolites or
q-space imaging, one may expect to reach new levels
and break new ground in the already flourishing field
of diffusion imaging.
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